A Quick Post on Math Learning

Some thoughts on class organization and learning.

I read something that I thought was interesting and rather than star it and email it to some interested folks, I thought I’d post it here.

I’m a big fan of Dan Meyer (dy/dan); his is probably the first blog I read on a regular basis and I’ve used some of his ideas in my classes.  He recently posted a discussion some philosophy behind teaching and learning math:

[Mailbag] Teaching Geometry Inductively V. Deductively

And while the whole post is worth reading, I’d like to point out one particular part:

We talked over here about “organizing principles” for a math class. I’d say “make math real world” is as self-defeating an organizing principle as one can find. “Prioritize perplexity,” on the other hand, lets us chase down curious mathematics wherever it lives, either in the world outside the classroom or in the world of numbers and shapes.

I find this to be a wonderful approach to structuring a course.  Don’t make it about the specific content, don’t make it about tools and applications, but make it about curiosity, perplexity and complexity. I don’t have all the details in mind, but I see a mix of exploration/experimentation, with conjectures (and the appropriate level of abstraction), and then proofs (as appropriate). All this with the expectation that whether the original source is ‘real world’ or not, by establishing this as the organizing principle will lead to mathematical results being held up as interesting and significant. For example, I’m imagining the scenario in Calculus when The Fundamental Theorem of Calculus is conjectured/revealed, that there is cheering in the aisles.

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